In this paper, miniaturized microstrip crossover circuits are proposed using slots shapes obtained using the superformula. The design starts by using a conventional half-wavelength square patch crossover. For miniaturization purposes, different superformula slot shapes are introduced on the square patch. The proposed crossovers are designed to operate at 2.4 GHz using a 0.8 mm thick FR-4 substrate with a relative permittivity of 4.4. The designs are simulated using the high frequency structure simulator (HFSS). One of the miniaturized designs is fabricated and its scattering parameters are measured using a vector network analyzer. Simulated and measured results agree very well. At the design frequency, the measured input port matching is better than ˗19 dB, while 𝑆12, 𝑆13 and 𝑆14 have the values of ˗12 dB, ˗2.2 dB and ˗10 dB, respectively. Furthermore, a 71% size reduction is achieved as compared to the conventional crossover area.

1. International Journal of Electrical and Computer Engineering (IJECE)
Vol. 12, No. 5, October 2022, pp. 5145~5152
ISSN: 2088-8708, DOI: 10.11591/ijece.v12i5.pp5145-5152  5145
Journal homepage: http://ijece.iaescore.com
Design of miniaturized patch crossover based on superformula
slot shapes
Mutaz Akram Banat, Nihad Ibrahim Dib
Department of Electrical Engineering, Jordan University of Science and Technology, Irbid, Jordan
Article Info ABSTRACT
Article history:
Received Oct 30, 2021
Revised Apr 8, 2022
Accepted May 5, 2022
In this paper, miniaturized microstrip crossover circuits are proposed using
slots shapes obtained using the superformula. The design starts by using a
conventional half-wavelength square patch crossover. For miniaturization
purposes, different superformula slot shapes are introduced on the square
patch. The proposed crossovers are designed to operate at 2.4 GHz using a
0.8 mm thick FR-4 substrate with a relative permittivity of 4.4. The designs
are simulated using the high frequency structure simulator (HFSS). One of
the miniaturized designs is fabricated and its scattering parameters are
measured using a vector network analyzer. Simulated and measured results
agree very well. At the design frequency, the measured input port matching
is better than ˗19 dB, while 𝑆12, 𝑆13 and 𝑆14 have the values of ˗12 dB,
˗2.2 dB and ˗10 dB, respectively. Furthermore, a 71% size reduction is
achieved as compared to the conventional crossover area.
Keywords:
Crossover
Microstrip patch
Superformula shapes
This is an open access article under the CC BY-SA license.
Corresponding Author:
Mutaz Akram Banat
Department of Electrical Engineering, Jordan University of Science and Technology
P. O. Box 3030, Irbid 22110, Jordan
Email: mutazbanat@yahoo.com
1. INTRODUCTION
The performance of wireless communications systems is usually affected by the large fluctuations in
the wireless signals which are caused by multi-path fading and interference. One way to overcome this is to
use smart antenna arrays. The capacity and range of the base-station can be improved by the use of switched
beam systems, which consist of fixed beamforming networks, without any modifications at the mobile unit.
The key component of such beamforming networks is the Butler matrix which is widely used in smart
antenna systems [1], [2]. Butler matrix is a passive reciprocal network that consists of couplers,
phase-shifters, and crossovers. One of the common problems in microwave integrated circuits is the crossing
transmission lines (TLs). To overcome this problem, crossover circuits are used whenever an intersection
between TLs carrying different signals at the same layer is unavoidable. Traditionally, air-bridges and wired
vias, which lead to non-planar structures and increase the fabrication complexity and cost, were used to
design crossovers [3], [4]. To overcome this, planar four ports crossover circuits that allow a pair of
intersecting lines to cross each other while achieving the required isolation between the two signal paths can
be used.
Fully planar cascaded hybrids were proposed in [5], while, in [6], zero-dB directional couplers were
designed. Symmetric four-port networks with good isolation between adjacent ports were presented in
[7]–[9]. The main disadvantage of such crossovers is the large occupational area at low frequencies on
printed circuit board (PCB) that limits their use in different applications. Therefore, several miniaturization
techniques were introduced to overcome this while maintaining the same performance in [10]–[14]. The use
of microstrip branch-line couplers (BLCs) for crossover applications was proposed in [10], where the goal

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was to find the impedance values to get the crossover operation of the BLC. Using multi-section BLC
enhances the performance and the bandwidth, but it suffers from several drawbacks, like its large size. New
compact BLC shapes were investigated to overcome these disadvantages. In [11], the proposed crossover
design used four arc-shaped slots and two perpendicular rectangular slots on the patch which resulted in 82%
reduction in the total size compared with the conventional crossover. In [12], a dual-band branch-line coupler
was presented where the BLC transmission lines were replaced by their equivalent T-/Pi-shaped networks. A
similar approach was used in [13] to design a miniaturized crossover. Dual-band planar crossover with two-
section BLC structure was proposed in [14], while, in [15], a multi-section BLC for crossover applications
was presented. Based on negative-refractive-index transmission line metamaterial lines, a miniaturized
crossover, with good performance, was proposed in [16]. In [17], a new planar dual-frequency crossover was
presented. In [18], a wideband crossover was presented based on the typical 2x2 distributed window-shaped
structure, while a miniaturized quad-band BLC crossover was proposed in [19]. In [20], a transmission line
model was proposed and used in the design of compact single and two-section BLCs at 0.85 GHz. In [21],
wideband crossovers with high selectivity were proposed based on stub-loaded ring resonators.
In this paper, the design of miniaturized patch crossover based on superformula slot shapes is
investigated. Different superformula slot shapes are proposed. The overall crossover occupation area reduced
by a factor of 71% of its original size.
2. RESEARCH METHOD
The conventional square crossover is shown in Figure 1. To design any crossover, the insertion loss
(between the opposite ports) should be minimized and the isolation (between adjacent ports) should be
maximized while maintaining compactness. In Figure 1, the microstrip patch along with the ground plane on
the other side of the substrate can be represented as a dielectric loaded cavity with perfect electric top and
bottom walls [22]. The thickness of the substrate is assumed to be very small compared to the wavelength
and the patch dimensions, thus, the only possible field configuration inside the cavity is the transverse
magnetic (TM) mode. The electric and magnetic fields inside the cavity can be written in terms of
the TM mn0 modes as (1), (2), (3) [23]:
EZ=A1cos (mπx/L)cos (nπy/L) (1)
Hx=A2cos (mπx/L)sin (nπy/L) (2)
Hy=A3sin (mπx/L)cos (nπy/L) (3)
where 𝐴𝑖 are the amplitudes of the field’s components, L is the length of the patch, and m, and n are the mode
numbers. Thus, the resonant frequency of the two fundamental modes TM100 and TM010 is given as (4):
fr=
c
2L√ℰr
(4)
where ℰ𝑟 is the substrate relative permittivity and c is the free-space speed of light. The magnetic field
components for the TM100 mode are:
Hy=A3sin (πx/L), Hx=0. (5)
for the TM010 mode, they are:
H𝑥=A2sin (πy/L), H𝑦=0. (6)
It is clear that these two modes have orthogonal magnetic fields. Based on the Poynting vector [24],
the signal flows in y-direction for the TM010 mode and in x-direction for the TM100 mode. Each face-to-face
pair of crossover ports (ports 1 and 3, or ports 2 and 4) must be properly aligned to couple one of the above
modes, which will maximize the isolation between the adjacent ports and will minimize the insertion loss
between the opposite ports.
2.1. Conventional square patch crossover design and experimental results
Assuming a resonant frequency of 2.4 GHz, the initial dimensions of the conventional square patch
crossover shown in Figure 1 are calculated using (4). Using FR-4 substrate (thickness 0.8 mm and 𝜖𝑟=4.4)

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and 50 Ω characteristic impedance for all ports, the following optimized dimensions are obtained:
W=64.7 mm, L=30.7 mm, Wf =1.53 mm. The total area for this crossover excluding the feeding lines is
9.4 𝑐𝑚2
. A picture of the fabricated crossover is shown in Figure 2. The design is simulated using the high
frequency structure simulator (HFSS), the simulated results are shown in Figure 3 and the measured ones
which were obtained using an E5071C ENA Keysight vector network analyzer are shown in Figure 4. At the
design frequency, simulated S-parameters: 𝑆11, 𝑆12, 𝑆13 and 𝑆14 have the values of ˗28 dB, ˗15 dB, ˗1.4 dB
and ˗15 dB, respectively. The measured results show 𝑆11better than ˗28 dB at the design frequency. The
experimental transmission parameters, 𝑆12, 𝑆13, and 𝑆14 are ˗14.5 dB, ˗2 dB and ˗16.5 dB at 2.4 GHz,
respectively. Table 1 shows the values of the simulated and measured S-parameters at 2.4 GHz.
Figure 1. Conventional square microstrip patch
crossover
Figure 2. Picture of the fabricated conventional
crossover
Figure 3. Simulated S-parameters of the crossover shown in Figure 2
Figure 4. Measured S-parameters of the crossover shown in Figure 2
Table 1. Measured and simulated S-parameters comparison at 2.4 GHz
S11(dB) S12(dB) S13(dB) S14(dB)
Simulated -28 -15 -1.4 -15
Experimental -28 -14.5 -2 -16.5

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2.2. Miniaturized square crossover using superformula shapes
In order to reduce the overall conventional crossover area, multiple slots shapes were investigated
like perpendicular lines and circular slot shape as proposed in [11]. In this paper, we use the superformula
generated slot shape. To the authors knowledge, the superformula was not used before to miniaturize the
crossover circuit. The superformula, known also as Gielis formula, is a geometrical expression that allows to
generate many geometrical shapes and forms [25]. The superformula expression contains seven different
parameters: a, b, 𝑁1,2,3 and 𝑚1,2 and it is given by the polar function of the form f= r(ɸ):
r(ɸ)=[|
1
𝑎
cos (
𝑚1
4
ɸ)|
𝑁2
+ |
1
𝑏
sin(
𝑚2
4
ɸ)|
𝑁3
]−1/𝑁1 (7)
The parameters a and b are chosen with different values to vary the distance of the inflection points
from the origin. The parameters 𝑁2 and 𝑁3 control the concavity of the curves between points, corners, and
sectors. The parameters 𝑚1,2 determine the number of points, corners, and sectors. Figure 5 shows different
shapes using different parameters values.
Figure 5. Examples of superformula shapes (a=1, b=1)
3. RESULTS AND DISCUSSION
3.1. Design #1
The first superformula slot shape is generated by using (7) with the following parameters,
a=b=1, 𝑚1=𝑚2 = 3, 𝑁1 =5, 𝑁2 = 𝑁3 =18. Figure 6 shows the HFSS layout for the proposed compact
crossover design with dimensions: W= 53 mm, L= 19 mm and W𝑓=1.53 mm. As shown in Figure 7, at the
design frequency, the simulated S-parameters: 𝑆11, 𝑆12, 𝑆13 and 𝑆14 have the values of ˗47 dB, ˗10 dB,
˗2.3 dB and ˗8 dB, respectively. The total area for this crossover excluding the ports dimensions is 3.6 𝑐𝑚2
,
which is equivalent to 38% of the conventional crossover size. In the next sections, different superformula
shapes will be investigated.
Figure 6. HFSS layout of a miniaturized crossover using superformula slot shape (design #1)
𝒎𝟏, 𝒎𝟐, 𝑵𝟏, 𝑵𝟐, 𝑵𝟑
4, 4, 0.26, 1.49, 1.49 7, 7, 3, 4, 1 8, 8, 1, 5, 8
3, 3, 2, 5, 7 2, 2, 8, 10, 4 4, 4, 1, 7, 8

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Figure 7. Simulated S-parameters of the miniaturized crossover shown in Figure 6
3.2. Design #2
The second superformula slot shape is generated by using (7) with the following parameters,
𝑎 = 𝑏 = 0.8, 𝑚1=𝑚2 = 8, 𝑁1 =3, 𝑁2 = 4, 𝑁3 = 7. Figure 8 shows the HFSS layout for the proposed
miniaturized crossover circuit with dimensions: W=52 mm, L=18 mm and W𝑓=1.53 mm. The simulated
scattering parameters are shown in Figure 9. At the design frequency, 𝑆11, 𝑆12, 𝑆13 and 𝑆14 have the values of
˗21.5 dB, ˗10 dB, ˗1.9 dB and ˗9.5 dB, respectively. The total area for this crossover excluding the ports
dimensions is 3.2 𝑐𝑚2
which is equivalent to 34% of the conventional crossover size.
Figure 8. HFSS layout of a miniaturized crossover using superformula slot shape (design #2)
Figure 9. Simulated S-parameters of the miniaturized crossover shown in Figure 8
3.3. Design #3
In this section, another superformula slot shape is investigated in order to achieve better
performance results and more size reduction. The slot shape is a combined one between the superformula
shape (𝑎 = 𝑏 = 1, 𝑚1=𝑚2 = 4, 𝑁1 = 0.26, 𝑁2 = 𝑁3 = 1.49) and two perpendicular rectangular slots with
some scaling to get the required resonant frequency. Figure 10 shows the HFSS layout for the proposed
miniaturized crossover with dimensions: W=50.5 mm, L=16.5 mm and 𝑤2=0.2 mm. Figure 11 shows the

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simulated scattering parameters. At the design frequency, 𝑆11, 𝑆12, 𝑆13, and 𝑆14 have the values of ˗21 dB,
˗11 dB, ˗1.8 dB and ˗10.6 dB, respectively. The total area for this crossover excluding the ports dimensions is
2.7 𝑐𝑚2
which is equivalent to 29% of the conventional crossover size.
Figure 10. HFSS layout of a miniaturized crossover using superformula slot shape (design #3)
Figure 11. Simulated S-parameters of the miniaturized crossover shown in Figure 10
This last crossover design is fabricated in Figure 12. Figure 13 presents the measured scattering
parameters, which shows a 𝑆11 better than ˗26 dB at the design frequency. The experimental transmission
parameters, 𝑆12, 𝑆13, and 𝑆14 are ˗12 dB, ˗2.2 dB and ˗10.5 dB at 2.4 GHz, respectively. Table 2 shows a
comparison between the above three superformula slot shapes performance and the size reduction compared
with the conventional square crossover using the same substrate and the resonant frequency. Table 3 shows a
comparison between the proposed miniaturized crossover (design #3) and some recently published
crossovers. For fair comparison, the area for each design is given in terms of the guided wavelength at the
design frequency.
Figure 12. Picture of the fabricated miniaturized crossover using superformula slot shape (design #3)

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Figure 13. Measured S-parameters of the miniaturized crossover shown in Figure 12
Table 2. A comparison between the simulated results of different miniaturization techniques of
conventional crossover
Miniaturization Method S11(dB) S12(dB) S13(dB) S14(dB) Size (𝑐𝑚2
)
Size reduction compared with
the conventional
Design #1 ˗47 ˗10 ˗2.3 ˗8 3.6 62%
Design #2 ˗21.5 ˗10 ˗1.9 ˗9.5 3.2 66%
Design #3 ˗21 ˗11 ˗1.8 ˗10.6 2.7 71%
Conventional square crossover ˗26 ˗17 ˗1.4 ˗17 9.4 NA
Table 3. Comparison of proposed crossover (design #3) with other published designs.
Ref Substrate Frequency (GHz) 𝑆11(𝑑𝐵) 𝑆12(𝑑𝐵) 𝑆13(𝑑𝐵) Size(𝜆𝑔 𝑥 𝜆𝑔)
[23] Rogers (thickness 0.64 mm &𝜖𝑟=10.2) 5.5 ˗25 ˗13 ˗ 0.9 (0.5x0.5)
[26] Rogers (thickness 0.64 mm &𝜖𝑟=10.2) 2.4 ˗27 ˗17 ˗1 (0.45x0.45)
[27] Rogers (thickness 0.508 mm &𝜖𝑟=3.55) 2.4 -17 -22 -1 (0.3x0.3)
[28] Rogers (thickness 0.508 mm &𝜖𝑟=2.65) 1.78 -22 -28 -0.6 (0.4x0.28)
[29] Rogers (thickness 0.635 mm &𝜖𝑟=10.2) 2.1-2.75 -11 -19 -1 (0.6x0.6)
Design #3 FR-4 Epoxy (thickness 0.8 mm &𝜖𝑟=4.4) 2.4 ˗21 ˗11 ˗1.8 (0.27x0.27)
4. CONCLUSION
In this paper, the physical area of the conventional microstrip patch crossover was reduced by 71%
using slot shapes inspired and further optimized through the utilization of superformula based geometries. A
very good agreement between the simulated and measured results was obtained. In general, the proposed
miniaturized crossovers have very good performance at the design frequency, and thus, can be used in
beamforming networks.
ACKNOWLEDGEMENTS
The authors are grateful to Eng. Nadia Tanash and Eng. Jehan Sheyyab from JUST EE Department
for their assistance during the fabrication and measurement stages. Special thanks for Eng. Omar Jibreel for
his advice and support throughout this work.
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BIOGRAPHIES OF AUTHORS
Mutaz Akram Banat received the B. Sc. degree in electrical engineering from
Jordan University of Science and Technology, Irbid, Jordan, in 2012. He received the
MSc degree in electrical engineering with the major of Wireless Communication from
Jordan University of science and Technology, Irbid, Jordan, in 2022. His research interests
include the computational electromagnetics, antennas, analysis and design of passive
microwave components, and optimization techniques. He can be contacted at email:
mutazbanat@yahoo.com.
Nihad Ibrahim Dib obtained his B. Sc. and M.Sc. in electrical engineering from
Kuwait University in 1985 and 1987, respectively. He obtained his Ph.D. in EE (major in
Electromagnetics) in 1992 from University of Michigan, Ann Arbor. Then, he worked as an
assistant research scientist in the radiation laboratory at the same school. In Sep. 1995, he
joined the EE department at Jordan University of Science and Technology (JUST) as an
assistant professor and became a full professor in Aug. 2006. His research interests are in
computational electromagnetics, antennas, and modeling of planar microwave circuits. He can
be contacted at email: nihad@just.edu.jo.